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IRC

Usually it is considered impolite to send unsolicited private messages on IRC.
As a result, it is usually tolerated to ask someone for a tipping bitcoin address in the public channel, which they may opt to answer to publicly or in private at their choice.

Third party services

ChangeTip is a great service that allows integrated bitcoin tipping on many sites:

Websites and Blogs

You'll sometimes notice a bitcoin address at the bottom of a webpage or a blog.
This is the address to send tips or donations to.
Note that this is generally considered a bad practice, but it is usually tolerated in this special case since no better solutions are usually available and tips don't generally need to be secure (see also: address reuse).

Misconstruing as spam

Bitcoin tipping can sometimes be misconstrued as spam.
To avoid this, it's best to be aware of your environment.
For example, when tipping on certain Reddit threads, it is best to contribute a logical comment along with the tip.

Remember, many people don't "get" bitcoin. There's a chance many people never will, in which case bitcoin becomes more of a backend protocol. Forcing bitcoin into people's faces isn't productive for anyone.